Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×#11725075 |
| derived, Sylow | C72 ⋊ C2×C9×C43 |
| Hall | C43×#89205 ⋊ C2 |
| Hall | C7×D7×C43 ⋊ C9 |
| Hall | C72×C43 ⋊ C2×C9 |
| Hall | #89205 ⋊ C2×C43 |
| Hall | C7×D7 ⋊ C9×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | #64422 |
| commutator, hypocenter | C72 | C2×C9×C43 |
| Frattini | C3 | C43×#64422 |
| Fitting, socle | C3×C72×C43 | C2×C3 |
| prime radical | C3×C7×D7×C43 | C3 |
| cosocle | C3×C72 | C2×C3×C43 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C43 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5418 |
2193 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 142);